BFS 搜索算法

Question

I am newly learning Python, and I am trying to create a bfs algorithm that can take vertices of a weighted graph and return the bfs. Eventually, I will need to add the weighted edges to the vertices so that I can calculate the distance travelled, however I am able to get the bfs to work with my vertices alone. This is the code so far:

# Python implementation to find the
# shortest path in the graph using
# dictionaries

# Function to find the shortest
# path between two nodes of a graph
def BFS_SP(graph, start, goal):
    
    explored = []
    
    # Queue for traversing the
    # graph in the BFS
    queue = [[start]]
    
    # If the desired node is
    # reached
    if start == goal:
        print("Same Node")
        return
    
    # Loop to traverse the graph
    # with the help of the queue
    while queue:
        path = queue.pop(0)
        node = path[-1]
        
        # Condition to check if the
        # current node is not visited
        if node not in explored:
            neighbours = graph[node]
            
            # Loop to iterate over the
            # neighbours of the node
            for neighbour in neighbours:
                new_path = list(path)
                new_path.append(neighbour)
                queue.append(new_path)
                
                # Condition to check if the
                # neighbour node is the goal
                if neighbour == goal:
                    print("Shortest path = ", *new_path)
                    return
            explored.append(node)

    # Condition when the nodes
    # are not connected
    print("So sorry, but a connecting"\
                " path doesn't exist :(")
    return
# Driver Code
if __name__ == "__main__":
    
    # Graph using dictionaries
    graph = {
        'Arad':             ['Zerind', 'Timisoara', 'Sibiu'],
        'Bucharest':        ['Urziceni', 'Giurgiu', 'Pitesti', 'Fagaras'],
        'Craiova':          ['Dobreta', 'Pitesti', 'Rimnicu Vilcea'],
        'Dobreta':          ['Mehadia', 'Craiova'],
        'Eforie':           ['Hirsova'],
        'Fagaras':          ['Sibiu', 'Bucharest'],
        'Giurgiu':          ['Bucharest'],
        'Hirsova':          ['Eforie', 'Urziceni'],
        'Iasi':             ['Neamt', 'Vaslui'],
        'Lugoj':            ['Mehadia', 'Timisoara'],
        'Mehadia':          ['Lugoj', 'Dobreta'],
        'Neamt':            ['Iasi'],
        'Oradea':           ['Zerind', 'Sibiu'],
        'Pitesti':          ['Rimnicu Vilcea', 'Bucharest', 'Craiova'],
        'Rimnicu Vilcea':   ['Sibiu', 'Pitesti', 'Craiova'],
        'Sibiu':            ['Rimnicu Vilcea', 'Fagaras', 'Arad', 'Oradea'],
        'Timisoara':        ['Lugoj', 'Arad'],
        'Urziceni':         ['Bucharest', 'Hirsova'],
        'Vaslui':           ['Iasi', 'Urziceni'],
        'Zerind':           ['Oradea', 'Arad']
    }
    
    # Function Call
    BFS_SP(graph, 'Arad', 'Bucharest')

I need my graph array to actually look like this instead:

graph = {
    'Arad':             [['Zerind', 75], ['Timisoara', 118], ['Sibiu', 140]],
    'Bucharest':        [['Urziceni', 85], ['Giurgiu', 90], ['Pitesti', 101], ['Fagaras', 211]],
    'Craiova':          [['Dobreta', 120], ['Pitesti', 138], ['Rimnicu Vilcea', 146]],
    'Dobreta':          [['Mehadia', 75], ['Craiova', 120]],
    'Eforie':           [['Hirsova', 86]],
    'Fagaras':          [['Sibiu', 99], ['Bucharest', 211]],
    'Giurgiu':          [['Bucharest', 90]],
    'Hirsova':          [['Eforie', 86], ['Urziceni', 98]],
    'Iasi':             [['Neamt', 87], ['Vaslui', 92]],
    'Lugoj':            [['Mehadia', 70], ['Timisoara', 111]],
    'Mehadia':          [['Lugoj', 70], ['Dobreta', 75]],
    'Neamt':            [['Iasi', 87]],
    'Oradea':           [['Zerind', 71], ['Sibiu', 151]],
    'Pitesti':          [['Rimnicu Vilcea', 97], ['Bucharest', 101], ['Craiova', 138]],
    'Rimnicu Vilcea':   [['Sibiu', 80], ['Pitesti', 97], ['Craiova', 146]],
    'Sibiu':            [['Rimnicu Vilcea', 80], ['Fagaras', 99], ['Arad', 140], ['Oradea', 151]],
    'Timisoara':        [['Lugoj', 111], ['Arad', 118]],
    'Urziceni':         [['Bucharest', 85], ['Hirsova', 98]],
    'Vaslui':           [['Iasi', 92], ['Urziceni', 142]],
    'Zerind':           [['Oradea', 71], ['Arad', 75]]
}

And I'm some what of a loss on how I can modify my code to take the new version of graph as individual nodes. If I implement my new graph as I need it into my old code, I receive an error that say:

Traceback (most recent call last):
  File "/Users/meikebuettner/hello/astar_test.py", line 79, in <module>
    BFS_SP(graph, 'Arad', 'Bucharest')
  File "/Users/meikebuettner/hello/astar_test.py", line 30, in BFS_SP
    neighbours = graph[node]
TypeError: unhashable type: 'list'

Any insight, help, idea or topic to research would be GREATLY appreciated! Thank you!!

Answer 1

The problem was caused by you adding nodes, which is a list in your new data structure, to new_path

for neighbour in neighbours: # neighbour: ['Rimnicu Vilcea', 97]
    ...
    new_path.append(neighbour)

new_path is expected to contain only the names of the nodes, not names and weights.

We can fix as:

for neighbour_node in neighbours:
    neighbour = neighbour_node[0]
    ...

Reasons for this suggestion:

• neighbour_node is more correct name than neighbour in this case because it represents the node, not the name of the neigbour.
• We can fix the comparison for neighbour and goal without modifying that line

# Condition to check if the
# neighbour node is the goal
if neighbour == goal:

Note: there are several ways to fix your code, mine is just one. You can try the others like changing the data structure of path and new_path .